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In modern mathematics teaching we want relational understanding, in addition to instrumental understanding. Describe how a teacher would teach for both instrumental and relational understanding of long division 357÷19.

Teaching long division of 357÷19 for instrumental understanding

Teaching long division of 357÷19 for relational understanding

A company makes products A and B. Each unit of product A requires 1 unit of resource 1 and 5 units

of resource 2. Each unit of product B requires 5 units of resource 1 and 4 units of resource 2. If there

are 40 units of resource 1 and 140 units of resource 2 available, how many units of each product should

be produced if all the resources are to be used?

Solve this system of equations and provide a graphical representation of the solution. (12)

x2 + y2 = 5

x + y = 1

3.1 Write a number sentence that will represent the structure of the following problem situations. 3.1.1 Nare had some marbles. After receiving 24 from his sister, he now has 52 marbles altogether. How many marbles did Nare have at the beginning? (2) 3.1.2 Gabriel and Miranda have R257 between them. Gabriel has R165. How much does Miranda have? (3.1.3 Shaheed bought 3 chickens for R94 each from a local supermarket. She also bought a bag of potatoes. Shaheed paid R282 in total. How much did the potatoes cost? (2) 3.1.4 Phumzile is 6 years younger than her brother, Piet. How old is Piet when Phumzile is 25 years old? (2) 3.1.5 The young ostrich, Lenka, has to take 3 steps to keep up with every step taken by her mother. How many steps must Lenka take when her mother takes 6 steps? (2) 3.1.6 Mashudu had R500 in his wallet. After buying some dinner for him and a friend, he now has R220. How much did Mashudu pay for the dinner? (2) 3.2 Name the problem type for each of the problem situations in 3.1.

Convert 16500 tonnes to kg/ha

State whether the following statement true or false

QUESTION 4

The number of arrivals per minute at a bank located in the central business district of a large city

was recorded over a period of 200 minutes, with the following results:

Arrivals Frequency

0 14

1 31

2 47

3 41

4 29

5 21

6 10

7 5

8 2

The probability of at least two arrivals per minute at the bank is 0:155:

QUESTION 26

A local fire station receives on average 8.5 emergency telephone calls per hour. Assume that

these calls are Poisson distributed. Calculate the probability that

(a) the fire station will get nine calls during one hour. (2)

(b) the fire station will get five to seven (inclusive) calls during one hour. (3)

(c) the fire station will get at least 4 calls during one hour. (3)

(d) the fire station will get more than 6 calls during one hour.

QUESTION 25

Suppose that X is a binomial random variable with n D 25 and p D 0:5: Calculate

(a) the probability P .X D 15/: (2)

(b) the probability P .X  16/: (4)

(c) the expected value of X. (2)

(d) the variance of X. (3)

QUESTION 24

According to a report from the research for Studying Health System Change, 20% of South Africans

delay or go without medical care because of concerns about cost. Suppose that 8 individuals are

randomly selected.

(a) What is the probability that two individuals will delay or go without medical care? (2)

(b) What is the probability that at most two individuals will delay or go without medical care? (3)

(c) What is the probability that at least seven individuals will delay or go without medical care?

(3)

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